Density of integers which are discriminants of cyclic fields of odd prime degree
โ Scribed by Blair K. Spearman; Kenneth S. Williams
- Book ID
- 105755202
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 81 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0003-889X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let L be a cyclic number field of prime degree p. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that an integral basis ฮ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in the pth
lGl=p", where n=n,+n,+. , . + n r 2 ) like 1) with apnn=b,, instead of apnn=l. Proof. Let G be a group of order p" with an elementary abelian normal subgroup B for which GIB is cyclic of order p"". Further let aB be a generating element of GIB. Then upnn B. The group (a) suffers from B a representat